I think that in a wooden boat that spends most of its time in the water that it would probably not be a good idea. But absent the electrolite (either salt or fresh water) most of the time, you shouldn't have a problem. Also without any electrical current on board you should have less to worry about. You could always attach zinc anodes to the bottom of the kayak.
Take a look at the article below.
http://www.yachtsurvey.com/corrosion.htm